In Greek mythology King Agamemnon of Mycenae, leader of the Greeks in the Trojan War, returns home victorious after the War, having captured the Trojan princess Cassandra to be his slave.

However, Agamemnon is no sooner home than his wife, Queen Clytemnestra, murders both Agamemnon and Cassandra.

Clytemnestra has several reasons to kill her husband Agamemnon: revenge for things he did before the War, to enjoy supreme power herself and to be free to live with her lover Aegisthus.

However, why does Clytemnestra kill Cassandra too?

If Clytemnestra loved her husband Agamemnon and wanted to be with him she might have resented Cassandra as a rival for his attention, yet that does not seem to apply as Clytemnestra does not love Agamemnon nor want to live with him as his wife.

Cassandra, an enslaved member of a conquered people, seems no threat. In that society where values were different from ours, Cassandra alive is valuable property, to be put to work or, if Clytemnestra already has enough slaves or does not want Cassandra around, to trade her for cattle or other things of value.

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CASSANDRA: This two-footed lioness, who mates with a wolf in the absence of the noble lion, will slay me, miserable as I am. Brewing as it were a drug, she vows that with her wrath she will mix requital for me too, while she whets her sword against her husband, to take murderous vengeance for bringing me here. Source: Agamemnon 1256 ff.

The two-footed lioness is Clytaemestra and the wolf is Aegisthus, Agamemnon's cousin, who was prophesied to be his killer.

CLYTAEMESTRA: Here lies the man who did me wrong, plaything of each Chryseis at Ilium; and here she lies, his captive, and auguress, and concubine, his oracular faithful whore, yet equally familiar with the seamen's benches. The pair has met no undeserved fate. For he lies thus; while she, who, like a swan, has sung her last lament in death, lies here, his beloved; but to me she has brought for my bed an added relish of delight.
Source: ibid. 1438 ff.

In the Aeschylus, Clytaemestra sees as both an insult and a threat. (In various places in the Troy cycle, Agamemnon talks about putting concubines above his wife.) So, jealousy in the form of resentment.

Although Cassandra laments in the Aeschylus play, she rejoices in this fate as a means of vengeance against the killer of her family:

CASSANDRA: O mother, crown my head with victor's wreaths; rejoice in my royal match; lead me and if you find me unwilling at all, thrust me there by force; for if Loxias is indeed a prophet, Agamemnon, that famous king of the Achaeans, will find in me a bride more vexatious than Helen. For I will slay him and lay waste his home to avenge my father's and my brothers' death.The Trojan Women 353 ff.

There are theories that Cassandra is the "net" cast upon Agamemnon in his bath, to tangle him up for the killing stroke. Euripides implies this is the case both symbolically, and potentially actually (does Cassandra struggle to keep Agamemnon from effectively defending himself?)

Robert Graves proposes a etymology of her name (although the second part of her name is Greek, the first has no direct root) which implies "tangler of men". Graves uses a contracted form of κατά+σωτήρ -- against salvation to pull from the water (i.e. fishing nets which are the death of the fish) + ἀνδρών "man"

This is a strong theory because nets are a symbol of the goddess in general, related to the Latin "matrix" (womb), and nets are widely and specifically referenced in conjunction with Agamemnon's death.

In some forms of the myth, it is Aigisthus who does the actual killing, per the prophecy that leads to his conception.

There are other, more obscure, versions of the myth in which Cassandra is not murdered.